When estimating the area covered by an object, what type of error might you make and what sources might have caused it? Can you do anything to reduce the amount of error that might occur?
What other sources of errors might you need to be aware of when conducting scientific investigations? How can you reduce error when you design experiments or make a measurement? Special Feature Type: Practices of Science. Further Investigations: What is an Invertebrate? Question Set: What is a Mammal? Further Investigations: What is a Mammal? Share and Connect. We invite you to share your thoughts, ask for help or read what other educators have to say by joining our community. Outliers need to be examined closely.
Sometimes, for some reason or another, they should not be included in the analysis of the data. It is possible that an outlier is a result of erroneous data. Other times, an outlier may hold valuable information about the population under study and should remain included in the data. The key is to carefully examine what causes a data point to be an outlier. We could guess at outliers by looking at a graph of the scatterplot and best fit line.
However, we would like some guideline as to how far away a point needs to be in order to be considered an outlier. As a rough rule of thumb, we can flag any point that is located further than two standard deviations above or below the best fit line as an outlier, as illustrated below. The standard deviation used is the standard deviation of the residuals or errors. Statistical outliers : This graph shows a best-fit line solid blue to fit the data points, as well as two extra lines dotted blue that are two standard deviations above and below the best fit line.
Note: There is no rigid mathematical definition of what constitutes an outlier; determining whether or not an observation is an outlier is ultimately a subjective exercise. The above rule is just one of many rules used. Another method often used is based on the interquartile range IQR. For example, some people use the [latex]1. This defines an outlier to be any observation that falls [latex]1. If we are to use the standard deviation rule, we can do this visually in the scatterplot by drawing an extra pair of lines that are two standard deviations above and below the best fit line.
Any data points that are outside this extra pair of lines are flagged as potential outliers. Or, we can do this numerically by calculating each residual and comparing it to twice the standard deviation.
Graphing calculators make this process fairly simple. Outliers can have many anomalous causes. A physical apparatus for taking measurements may have suffered a transient malfunction. There may have been an error in data transmission or transcription. Outliers arise due to changes in system behavior, fraudulent behavior, human error, instrument error or simply through natural deviations in populations. For example, a test for a disease may report a negative result, when the patient is, in fact, infected.
This is a type II error because we accept the conclusion of the test as negative, even though it is incorrect. In statistical analysis, a type I error is the rejection of a true null hypothesis, whereas a type II error describes the error that occurs when one fails to reject a null hypothesis that is actually false.
The error rejects the alternative hypothesis, even though it does not occur due to chance. A type II error, also known as an error of the second kind or a beta error, confirms an idea that should have been rejected, such as, for instance, claiming that two observances are the same, despite them being different.
A type II error does not reject the null hypothesis, even though the alternative hypothesis is the true state of nature. In other words, a false finding is accepted as true. A type II error can be reduced by making more stringent criteria for rejecting a null hypothesis. Taking these steps, however, tends to increase the chances of encountering a type I error—a false positive result.
When conducting a hypothesis test, the probability or risk of making a type I error or type II error should be considered. The steps taken to reduce the chances of encountering a type II error tend to increase the probability of a type I error. The difference between a type II error and a type I error is that a type I error rejects the null hypothesis when it is true i. The probability of committing a type I error is equal to the level of significance that was set for the hypothesis test.
Therefore, if the level of significance is 0. The probability of committing a type II error is equal to one minus the power of the test, also known as beta. The power of the test could be increased by increasing the sample size, which decreases the risk of committing a type II error.
Assume a biotechnology company wants to compare how effective two of its drugs are for treating diabetes. The null hypothesis states the two medications are equally effective. A null hypothesis, H 0 , is the claim that the company hopes to reject using the one-tailed test. Syntax errors are the easiest to find and correct. The compiler will tell you where it got into trouble, and its best guess as to what you did wrong. Usually the error is on the exact line indicated by the compiler, or the line just before it; however, if the problem is incorrectly nested braces, the actual error may be at the beginning of the nested block.
If there are no syntax errors, Java may detect an error while your program is running. You will get an error message telling you the kind of error, and a stack trace that tells not only where the error occurred, but also what other method or methods you were in. For example,.
0コメント